Greg, from my experience, cold will not cause you a problem. If the pump is pumping, water will come out somewhere, but you may not like it.
Moss grows in my sump pit and occasionally clogs the plastic tube to the pressure switch that makes the pump start and stop. Since I clean out the pit (not a pleasant job, dipping your hand into the cold water and prying the moss off the inside of the pit) when I clean the line, I don't get enough moss that it clogs the pump intake.
I have an old cast iron pump that I have replaced once, when it was about 25 years old. I don't think that the new pumps are made as well and you probably have to replace them more often--about every 5-10 years from what I hear. But the new ones cost a lot less than my old iron monster.
One little note on this subject, sump pumps have to be on theirown electric circuit. It might be tempting to put a light socket or wall plug on the same line as the sump pump, but don't do it or you will be changing it later. And because of the proximity to water, it is not a good idea anyway.